August 2017 September 2017 October 2017 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 3 4 5 1 2 1 2 3 4 5 6 7 6 7 8 9 10 11 12 3 4 5 6 7 8 9 8 9 10 11 12 13 14 13 14 15 16 17 18 19 10 11 12 13 14 15 16 15 16 17 18 19 20 21 20 21 22 23 24 25 26 17 18 19 20 21 22 23 22 23 24 25 26 27 28 27 28 29 30 31 24 25 26 27 28 29 30 29 30 31 |

4:00 pm Friday, September 15, 2017 Undergraduate Colloquium: Primes within arithmetic progressionsby Anthony Varilly-Alvarado (Rice) in HBH 227- Dirichlet's Theorem on arithmetic progressions says that sequences of numbers like 2, 5, 8, 11, 14, 17, 20, etc contain infinitely many prime numbers (in this case 2, 5, 11, 17, etc). More precisely, it says that if an arithmetic progression has a first term and a common difference that share no prime factors, then within the progression there are infinitely many prime numbers. I will prove Dirichlet's theorem for the sequence 1, 5, 9, 13, 17, 21, etc, following the argument of Dirichlet's proof. The full proof involves a heavy mixture of complex analysis, group character theory, and tricky estimates. The particular case I will show contains all the features of the proof, but the details are simple enough to be understood by a student who has taken Math 102.
Submitted by sswang@rice.edu |